29.12.23 problem 342

Internal problem ID [4942]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 342
Date solved : Tuesday, January 28, 2025 at 02:40:33 PM
CAS classification : [_rational, _Abel]

\begin{align*} \left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 126

dsolve((b*x+a)^2*diff(y(x),x)+c*y(x)^2+(b*x+a)*y(x)^3 = 0,y(x), singsol=all)
 

\[ \frac {\left (a \sqrt {b}+b^{{3}/{2}} x \right ) {\mathrm e}^{-\frac {\left (\left (-b x -a +c \right ) y \left (x \right )+b \left (b x +a \right )\right ) \left (\left (b x +a +c \right ) y \left (x \right )+b \left (b x +a \right )\right )}{2 y \left (x \right )^{2} \left (b x +a \right )^{2} b}}+\frac {c \sqrt {2}\, \sqrt {\pi }\, {\mathrm e}^{\frac {1}{2 b}} \operatorname {erf}\left (\frac {\sqrt {2}\, \left (c y \left (x \right )+b \left (b x +a \right )\right )}{2 \sqrt {b}\, y \left (x \right ) \left (b x +a \right )}\right )}{2}+b^{{3}/{2}} c_{1}}{b^{{3}/{2}}} = 0 \]

✓ Solution by Mathematica

Time used: 1.329 (sec). Leaf size: 149

DSolve[(a+b x)^2 D[y[x],x]+c y[x]^2+(a+b x)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {c}{\sqrt {-b (a+b x)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}\right )^2\right )}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]