74.15.58 problem 58

Internal problem ID [16497]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 58
Date solved : Tuesday, January 28, 2025 at 09:09:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
 

\[ y = c_{2} \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right ) c_{1} +\frac {x^{2}}{5} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 55

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

\[ y(x)\to \cos (\log (x)) \int _1^x-K[1] \sin (\log (K[1]))dK[1]+\sin (\log (x)) \int _1^x\cos (\log (K[2])) K[2]dK[2]+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \]