35.6.31 problem 37

Internal problem ID [6181]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 37
Date solved : Monday, January 27, 2025 at 01:46:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

\[ y = -3+\left (c_1 x +c_2 \right ) {\mathrm e}^{-x}+\frac {\left (-3 x +5\right ) {\mathrm e}^{2 x}}{27}+x +{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.654 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{27} e^{2 x} (5-3 x)+e^x+x+e^{-x} (c_2 x+c_1)-3 \]