Internal problem ID [2172]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 y^{\prime \prime }+5 y^{\prime }-3 y=\sin \left (x \right )-8 x} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve([2*diff(y(x),x$2)+5*diff(y(x),x)-3*y(x)=sin(x)-8*x,y(0) = 1/2, D(y)(0) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {8 \,{\mathrm e}^{-3 x} \left (-\frac {51 \,{\mathrm e}^{\frac {7 x}{2}}}{35}+\frac {13}{840}+\left (x -\frac {3 \cos \left (x \right )}{80}-\frac {3 \sin \left (x \right )}{80}+\frac {5}{3}\right ) {\mathrm e}^{3 x}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 38
DSolve[{2*y''[x]+5*y'[x]-3*y[x]==Sin[x]-8*x,{y[0]==1/2,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{630} \left (1680 x+26 e^{-3 x}-2448 e^{x/2}-63 \sin (x)-63 \cos (x)+2800\right ) \]