64.5.19 problem 19

Internal problem ID [13332]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 05:22:37 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-2 y&=2 x^{4} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

dsolve([x*diff(y(x),x)-2*y(x)=2*x^4,y(2) = 8],y(x), singsol=all)
 

\[ y = x^{2} \left (x^{2}-2\right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 14

DSolve[{x*D[y[x],x]-2*y[x]==2*x^4,{y[2]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (x^2-2\right ) \]