29.15.19 problem 427

Internal problem ID [5025]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 427
Date solved : Monday, January 27, 2025 at 10:04:08 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y&=a x +b x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 50

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {-b \left (-{\mathrm e}^{b \,x^{2}} c_{1} b +a \right )}}{b} \\ y \left (x \right ) &= -\frac {\sqrt {-b \left (-{\mathrm e}^{b \,x^{2}} c_{1} b +a \right )}}{b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.873 (sec). Leaf size: 98

DSolve[y[x] D[y[x],x]==a x+b x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-a+e^{b \left (x^2+2 c_1\right )}}}{\sqrt {b}} \\ y(x)\to \frac {\sqrt {-a+e^{b \left (x^2+2 c_1\right )}}}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}