12.24 problem 343

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*}