29.15.16 problem 424

Internal problem ID [5022]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 424
Date solved : Monday, January 27, 2025 at 10:04:00 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 61

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

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {4 \,{\mathrm e}^{2 b x} c_{1} b^{2}-4 b x a -2 a}}{2 b} \\ y \left (x \right ) &= \frac {\sqrt {4 \,{\mathrm e}^{2 b x} c_{1} b^{2}-4 b x a -2 a}}{2 b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 13.670 (sec). Leaf size: 77

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

\begin{align*} y(x)\to -\frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b} \\ y(x)\to \frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b} \\ \end{align*}