15.14.7 problem 7

Internal problem ID [3179]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:25:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

\[ y = {\mathrm e}^{\frac {\left (-3+\sqrt {17}\right ) x}{2}} c_2 +{\mathrm e}^{-\frac {\left (3+\sqrt {17}\right ) x}{2}} c_{1} -\frac {\sin \left (2 x \right )}{12}-\frac {\cos \left (2 x \right )}{12} \]

✓ Solution by Mathematica

Time used: 0.375 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]+3*D[y[x],x]-2*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{12} \cos (2 x)+e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (c_2 e^{\sqrt {17} x}+c_1\right )-\frac {1}{6} \sin (x) \cos (x) \]