69.1.43 problem 62

Internal problem ID [14196]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 62
Date solved : Tuesday, January 28, 2025 at 06:21:32 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve(diff(y(x),x)-n/x*y(x)=exp(x)*x^n,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 15

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

\[ y(x)\to \left (e^x+c_1\right ) x^n \]