29.1.10 problem 9

Internal problem ID [4617]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 9
Date solved : Monday, January 27, 2025 at 09:26:24 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 32

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

\[ y(x)\to -\frac {a \left (b x^3+3\right )}{b^2}+c_1 e^{\frac {b x^3}{3}} \]