64.13.25 problem 25

Internal problem ID [13555]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 05:52:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=10 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 22

dsolve([x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=10*x^2,y(1) = 1, D(y)(1) = -6],y(x), singsol=all)
 

\[ y = \frac {2 \ln \left (x \right ) x^{5}-x^{5}+2}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

DSolve[{x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==10*x^2,{y[1]==1,Derivative[1][y][1]==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x^5+2 x^5 \log (x)+2}{x^3} \]