77.1.126 problem 153 (page 236)

Internal problem ID [18016]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 153 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:19:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=x^2,y(x), singsol=all)
 

\[ y = \frac {3}{8}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{2 x}+\frac {x^{2}}{4}+\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 37

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

\[ y(x)\to \frac {1}{8} \left (2 x^2+4 x+3\right )+c_1 e^{2 x}+c_2 e^{2 x} x \]