64.13.24 problem 24

Internal problem ID [13554]
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 : 24
Date solved : Tuesday, January 28, 2025 at 05:52:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=-6 x^{3}+4 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=4\\ y^{\prime }\left (2\right )&=-1 \end{align*}

✓ Solution by Maple

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

dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=4*x^2-6*x^3,y(2) = 4, D(y)(2) = -1],y(x), singsol=all)
 

\[ y = -\frac {23}{24} x^{4}+3 x^{3}-2 x^{2}+\frac {5}{3} x \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 28

DSolve[{x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==4*x^2-6*x^3,{y[2]==4,Derivative[1][y][2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {23 x^4}{24}+3 x^3-2 x^2+\frac {5 x}{3} \]