Internal problem ID [12484]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=x^{2}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {11}{4}}, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=x^2,y(0) = 11/4, D(y)(0) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{2}+\frac {x}{2}+\frac {7 \,{\mathrm e}^{2 x}}{6}+\frac {7 \,{\mathrm e}^{-x}}{3}-\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 33
DSolve[{y''[x]-y'[x]-2*y[x]==x^2,{y[0]==11/4,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} \left (-6 x^2+6 x+28 e^{-x}+14 e^{2 x}-9\right ) \]