Internal problem ID [3091]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 343.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-b \,x^{2} y-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 21
dsolve(x^3*diff(y(x),x) = a+b*x^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a}{x^{2} \left (2+b \right )}+x^{b} c_{1} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 23
DSolve[x^3 y'[x]==a + b x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a}{(b+2) x^2}+c_1 x^b \\ \end{align*}