Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
79101	Solve the Differential Equation	(dx)/(dt)=1+t-x-tx	$\frac{d x}{d t} = 1 + t - x - t x$
79102	Solve the Differential Equation	y''''''''''''-6y''''''''-y''''+6y=0	$y'''''' - 6 y'''' - y'' + 6 y = 0$
79103	Solve the Differential Equation	2(dy)/(dx)-4xy=5x	$2 \frac{d y}{d x} - 4 x y = 5 x$
79104	Solve the Differential Equation	(y^2-1)xdx+(x^2+3)(yd)y=0	$(y^{2} - 1) x d x + (x^{2} + 3) yd y = 0$
79105	Solve the Differential Equation	y''''=(1-x-y)/(x+y)	$y'' = \frac{1 - x - y}{x + y}$
79106	Solve the Differential Equation	2y''''=(xy+y^2)/(x^2)	$2 y'' = \frac{x y + y^{2}}{x^{2}}$
79107	Solve the Differential Equation	xy''''+sin(y)+y=3	$x y'' + \sin (y) + y = 3$
79108	Solve the Differential Equation	(xy+y^2)dy=y^2dx	$(x y + y^{2}) d y = y^{2} d x$
79109	Solve the Differential Equation	x(yd)y=(x^2+y^2)dx	$x yd y = (x^{2} + y^{2}) d x$
79110	Solve the Differential Equation	(dy)/(dx)=5x^2+4/x , y(0)=1	$\frac{d y}{d x} = 5 x^{2} + \frac{4}{x}$ , $y (0) = 1$
79111	Solve the Differential Equation	y''''+5y=7x+1	$y'' + 5 y = 7 x + 1$
79112	Solve the Differential Equation	(dy)/(dx)+2x=5	$\frac{d y}{d x} + 2 x = 5$
79113	Solve the Differential Equation	(d^2y)/(dx^2)-4y=4e^(-x)	$\frac{d^{2} y}{d x^{2}} - 4 y = 4 e^{- x}$
79114	Solve the Differential Equation	(dQ)/(dx)=8/5x^(3/5)	$\frac{d Q}{d x} = \frac{8}{5} x^{\frac{3}{5}}$
79115	Solve the Differential Equation	y''''''''=2x	$y'''' = 2 x$
79116	Solve the Differential Equation	x^2(d^2y)/(dx^2)-7x(dy)/(dx)+16y=0	$x^{2} \frac{d^{2} y}{d x^{2}} - 7 x \frac{d y}{d x} + 16 y = 0$
79117	Solve the Differential Equation	(du)/(dt)=(d^2u)/(dx^2)	$\frac{d u}{d t} = \frac{d^{2} u}{d x^{2}}$
79118	Solve the Differential Equation	(dy)/y=x^20dx	$\frac{d y}{y} = x^{20} d x$
79119	Solve the Differential Equation	x(x+y)dy-y^2dx=0	$x (x + y) d y - y^{2} d x = 0$
79120	Solve the Differential Equation	(2x+x^3+3y)dx+(3x+2y)dy=0	$(2 x + x^{3} + 3 y) d x + (3 x + 2 y) d y = 0$
79121	Solve the Differential Equation	x^2y''''+3xy=1	$x^{2} y'' + 3 x y = 1$
79122	Solve the Differential Equation	(dr)/(dtheta)+r*sec(theta)=cos(theta)	$\frac{d r}{d θ} + r \cdot \sec (θ) = \cos (θ)$
79123	Solve the Differential Equation	y^2 natural log of ydy=sin(xdx)	$y^{2} \ln (yd y) = \sin (x d x)$
79124	Solve the Differential Equation	(dy)/(dx)=y/x+2	$\frac{d y}{d x} = \frac{y}{x} + 2$
79125	Solve the Differential Equation	(d^3y)/(dx^3)=e^(-x)	$\frac{d^{3} y}{d x^{3}} = e^{- x}$
79126	Solve the Differential Equation	(dy)/(dx)=6x^(7/9)	$\frac{d y}{d x} = 6 x^{\frac{7}{9}}$
79127	Solve the Differential Equation	y''''+y=7sin(x)	$y'' + y = 7 \sin (x)$
79128	Solve the Differential Equation	(dy)/(dt) = square root of yt	$\frac{d y}{d t} = \sqrt{y t}$
79129	Solve the Differential Equation	(2+x)(dy)/(dx)-xy=0	$(2 + x) \frac{d y}{d x} - x y = 0$
79130	Solve the Differential Equation	(df)/(dx)=-5x^2-5e^x , f(0)=-16	$\frac{d f}{d x} = - 5 x^{2} - 5 e^{x}$ , $f (0) = - 16$
79131	Solve the Differential Equation	(dy)/(dx)=ysin(x) where f(2pi)=1	$\frac{d y}{d x} = y \sin (x)$ where $f (2 π) = 1$
79132	Solve the Differential Equation	(dy)/(dx)=1/(x square root of 49x^2-1)	$\frac{d y}{d x} = \frac{1}{x \sqrt{49 x^{2} - 1}}$
79133	Solve the Differential Equation	(dx)/(1-x)+(dy)/(cos(y)^2)=0	$\frac{d x}{1 - x} + \frac{d y}{\cos^{2} (y)} = 0$
79134	Solve the Differential Equation	f(x)=x^3+2x^2-5x-6	$f (x) = x^{3} + 2 x^{2} - 5 x - 6$
79135	Solve the Differential Equation	(x^2y+x)dy=(y-y^2x)dx	$(x^{2} y + x) d y = (y - y^{2} x) d x$
79136	Solve the Differential Equation	y''''+y-x^2-2x=0	$y'' + y - x^{2} - 2 x = 0$
79137	Solve the Differential Equation	(du)/(dx)=6x^5-3x^2+9	$\frac{d u}{d x} = 6 x^{5} - 3 x^{2} + 9$
79138	Solve the Differential Equation	(dy)/(dx)=-y/x+3x	$\frac{d y}{d x} = - \frac{y}{x} + 3 x$
79139	Solve the Differential Equation	(y^4+2y)dx+(xy^3+2y^4-4x)dy=0	$(y^{4} + 2 y) d x + (x y^{3} + 2 y^{4} - 4 x) d y = 0$
79140	Solve the Differential Equation	(dy)/(dx)=21-y	$\frac{d y}{d x} = 21 - y$
79141	Solve the Differential Equation	(dy)/(dx)+y/5=0	$\frac{d y}{d x} + \frac{y}{5} = 0$
79142	Solve the Differential Equation	(dy)/(dx)=x^3 , y(0)=4	$\frac{d y}{d x} = x^{3}$ , $y (0) = 4$
79143	Solve the Differential Equation	(dy)/(dx)=xcos(8x^2) , y(0)=8	$\frac{d y}{d x} = x \cos (8 x^{2})$ , $y (0) = 8$
79144	Solve the Differential Equation	y''''''''''''-2y''''''''-y''''+2y=e^(3x)	$y'''''' - 2 y'''' - y'' + 2 y = e^{3 x}$
79145	Solve the Differential Equation	(2xy^3+1)dx+(3x^2y^2-y^-1)dy=0	$(2 x y^{3} + 1) d x + (3 x^{2} y^{2} - y^{- 1}) d y = 0$
79146	Solve the Differential Equation	(e^x)dx+((x)(e^y)+2y)dy=0	$(e^{x}) d x + ((x) (e^{y}) + 2 y) d y = 0$
79147	Solve the Differential Equation	4xy''''-y=0	$4 x y'' - y = 0$
79148	Solve the Differential Equation	(dy)/(dx)=y/x+3x	$\frac{d y}{d x} = \frac{y}{x} + 3 x$
79149	Solve the Differential Equation	(dy)/(dx)=4/(x-6)	$\frac{d y}{d x} = \frac{4}{x - 6}$
79150	Solve the Differential Equation	(dy)/(dx)=6x^(3/7)	$\frac{d y}{d x} = 6 x^{\frac{3}{7}}$
79151	Solve the Differential Equation	f(x)=(2/3x^2+4/5x-2/3)^2	$f (x) = {(\frac{2}{3} x^{2} + \frac{4}{5} x - \frac{2}{3})}^{2}$
79152	Solve the Differential Equation	(dy)/(dx)=e^(x+y)+x^2e^(x^3)+y	$\frac{d y}{d x} = e^{x + y} + x^{2} e^{x^{3}} + y$
79153	Solve the Differential Equation	(dy)/(dx)=(5x^2)/( square root of 8+x^3)	$\frac{d y}{d x} = \frac{5 x^{2}}{\sqrt{8 + x^{3}}}$
79154	Solve the Differential Equation	(dR)/(dx)=a(R^2+9)	$\frac{d R}{d x} = a (R^{2} + 9)$
79155	Solve the Differential Equation	y''''-4y=3	$y'' - 4 y = 3$
79156	Solve the Differential Equation	x''''=-x	$x'' = - x$
79157	Solve the Differential Equation	y''''=-1/(2y)	$y'' = - \frac{1}{2 y}$
79158	Solve the Differential Equation	x(dy)/(dx)=(1+x)(1+y)	$x \frac{d y}{d x} = (1 + x) (1 + y)$
79159	Solve the Differential Equation	(dy)/(dx)+6xy=12x	$\frac{d y}{d x} + 6 x y = 12 x$
79160	Solve the Differential Equation	(x+4y+3)dx=(2x-y-3)dy	$(x + 4 y + 3) d x = (2 x - y - 3) d y$
79161	Solve the Differential Equation	The (dy)/(dx) for y = square root of e^xsin(x)	The $\frac{d y}{d x}$ for $y = \sqrt{e^{x} \sin (x)}$
79162	Solve the Differential Equation	(dy)/(dt)=5 square root of t , y(1)=5	$\frac{d y}{d t} = 5 \sqrt{t}$ , $y (1) = 5$
79163	Solve the Differential Equation	(dy)/(dx)+12xy^4=0	$\frac{d y}{d x} + 12 x y^{4} = 0$
79164	Solve the Differential Equation	y''''=1/(2y)	$y'' = \frac{1}{2 y}$
79165	Solve the Differential Equation	5e^(y/x)(1-y/x)dx-(1+4e^(y/x))dy=0	$5 e^{\frac{y}{x}} (1 - \frac{y}{x}) d x - (1 + 4 e^{\frac{y}{x}}) d y = 0$
79166	Solve the Differential Equation	xdx+(x^2y+4y)dy=0	$x d x + (x^{2} y + 4 y) d y = 0$
79167	Solve the Differential Equation	y''''-2y/x=7	$y'' - 2 \frac{y}{x} = 7$
79168	Solve the Differential Equation	x(yd)x-(x^2+3y^2)dy=0	$x yd x - (x^{2} + 3 y^{2}) d y = 0$
79169	Solve the Differential Equation	(du)/(dx)=6x^5-5x^4+5	$\frac{d u}{d x} = 6 x^{5} - 5 x^{4} + 5$
79170	Solve the Differential Equation	(dy)/(dx)+ytan(x)=cos(x)^2	$\frac{d y}{d x} + y \tan (x) = \cos^{2} (x)$
79171	Solve the Differential Equation	xy''''+y=x natural log of x	$x y'' + y = x \ln (x)$
79172	Solve the Differential Equation	(dy)/(dx)=54yx^17	$\frac{d y}{d x} = 54 y x^{17}$
79173	Solve the Differential Equation	(dy)/(dx)=8x+8 , y(-1)=0	$\frac{d y}{d x} = 8 x + 8$ , $y (- 1) = 0$
79174	Solve the Differential Equation	5y''''+y=0	$5 y'' + y = 0$
79175	Solve the Differential Equation	4y''''+2y''''+27y=0	$4 y'' + 2 y'' + 27 y = 0$
79176	Solve the Differential Equation	4(d^2y)/(dx^2)+(dy)/(dx)=0	$4 \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} = 0$
79177	Solve the Differential Equation	4+3y''''=0	$4 + 3 y'' = 0$
79178	Solve the Differential Equation	f(x)=-7	$f (x) = - 7$
79179	Solve the Differential Equation	(dy)/(dx)=e^yx	$\frac{d y}{d x} = e^{y} x$
79180	Solve the Differential Equation	(dy)/(dx)=5x^4-2x^3+x^2	$\frac{d y}{d x} = 5 x^{4} - 2 x^{3} + x^{2}$
79181	Solve the Differential Equation	(dz)/(dx)+2z=4x	$\frac{d z}{d x} + 2 z = 4 x$
79182	Solve the Differential Equation	2x^3dy=y(2x^2+y^2)dx	$2 x^{3} d y = y (2 x^{2} + y^{2}) d x$
79183	Solve the Differential Equation	(dy)/(dx)=sin(x) , y(0)=4	$\frac{d y}{d x} = \sin (x)$ , $y (0) = 4$
79184	Solve the Differential Equation	y''''=-(9x)/(16y)	$y'' = - \frac{9 x}{16 y}$
79185	Solve the Differential Equation	y(x^2-y^2+1)dx-x(x^2-y^2-1)dy=0	$y (x^{2} - y^{2} + 1) d x - x (x^{2} - y^{2} - 1) d y = 0$
79186	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y^2) , y(0)=2	$\frac{d y}{d x} = \frac{x^{2}}{y^{2}}$ , $y (0) = 2$
79187	Solve the Differential Equation	(dy)/(dx)+2/xy=x^2	$\frac{d y}{d x} + \frac{2}{x} y = x^{2}$
79188	Solve the Differential Equation	(dy)/((y-1)^2)=dx	$\frac{d y}{{(y - 1)}^{2}} = d x$
79189	Solve the Differential Equation	(dy)/(dx)=2-3y	$\frac{d y}{d x} = 2 - 3 y$
79190	Solve the Differential Equation	(2x+y)dy=(x+2y)dx	$(2 x + y) d y = (x + 2 y) d x$
79191	Solve the Differential Equation	(dy)/(dx)=(e^(4x))/(y^3)	$\frac{d y}{d x} = \frac{e^{4 x}}{y^{3}}$
79192	Solve the Differential Equation	(dy)/(dx)+xe^x=0	$\frac{d y}{d x} + x e^{x} = 0$
79193	Solve the Differential Equation	y''''''''=e^xsin(x)	$y'''' = e^{x} \sin (x)$
79194	Solve the Differential Equation	(du)/(dx)=(sec(x^5)^2)(5x^4)	$\frac{d u}{d x} = (\sec^{2} (x^{5})) (5 x^{4})$
79195	Solve the Differential Equation	(dy)/(dx)=(6+x)(2+y)	$\frac{d y}{d x} = (6 + x) (2 + y)$
79196	Solve the Differential Equation	(y-x)dx-(y+x)dy=0	$(y - x) d x - (y + x) d y = 0$
79197	Solve the Differential Equation	y''''=1/2(y^2-1)	$y'' = \frac{1}{2} (y^{2} - 1)$
79198	Solve the Differential Equation	1/(x^4)*y''''=1	$\frac{1}{x^{4}} \cdot y'' = 1$
79199	Solve the Differential Equation	2y''''-3y=5	$2 y'' - 3 y = 5$
79200	Solve the Differential Equation	(3x^2+7y^2)dx+14x(yd)y=0	$(3 x^{2} + 7 y^{2}) d x + 14 x yd y = 0$