1.10 problem 9

Internal problem ID [2764]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 1
Problem number: 9.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }-x^{2} \left (a \,x^{3}+b y\right )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 29

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

\[ y \relax (x ) = -\frac {x^{3} a}{b}-\frac {3 a}{b^{2}}+{\mathrm e}^{\frac {b \,x^{3}}{3}} c_{1} \]

Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 32

DSolve[y'[x]==x^2*(a*x^3+b*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {a \left (b x^3+3\right )}{b^2}+c_1 e^{\frac {b x^3}{3}} \\ \end{align*}