28.2.36 problem 36

Internal problem ID [4479]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 36
Date solved : Monday, January 27, 2025 at 09:20:37 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \left (1+x \right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=(1+x)*exp(x)+2*exp(2*x)+3*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.354 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==(1+x)*Exp[x]+2*Exp[2*x]+3*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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