29.12.24 problem 343

Internal problem ID [4943]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 343
Date solved : Monday, January 27, 2025 at 09:53:14 AM
CAS classification : [_linear]

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

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 23

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

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