77.1.127 problem 154 (page 236)

Internal problem ID [18017]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 154 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=exp(x)+exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 45

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==Exp[x]+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{12} e^x \left (3 e^x+6 e^x \log \left (e^x\right )-4\right )+c_1 e^{2 x}+c_2 e^{4 x} \]