74.15.28 problem 28

Internal problem ID [16467]
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 : 28
Date solved : Tuesday, January 28, 2025 at 09:08:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+36 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+36*y(x)=x^2,y(x), singsol=all)
 

\[ y = \sin \left (6 \ln \left (x \right )\right ) c_{2} +\cos \left (6 \ln \left (x \right )\right ) c_{1} +\frac {x^{2}}{40} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 72

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+36*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (6 \log (x)) \int _1^x-\frac {1}{6} K[1] \sin (6 \log (K[1]))dK[1]+\sin (6 \log (x)) \int _1^x\frac {1}{6} \cos (6 \log (K[2])) K[2]dK[2]+c_1 \cos (6 \log (x))+c_2 \sin (6 \log (x)) \]