29.1.11 problem 10

Internal problem ID [4618]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 10
Date solved : Monday, January 27, 2025 at 09:26:26 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=a \,x^{n} y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x) = a*x^n*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 27

DSolve[D[y[x],x]==a*x^n*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{\frac {a x^{n+1}}{n+1}} \\ y(x)\to 0 \\ \end{align*}