Internal problem ID [13678]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.6 (ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-8 y=8 x^{2}-3} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)+2*diff(y(x),x)-8*y(x)=8*x^2-3,y(0) = 1, D(y)(0) = -3],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-4 \,{\mathrm e}^{4 x} x^{2}+{\mathrm e}^{6 x}-2 \,{\mathrm e}^{4 x} x +3\right ) {\mathrm e}^{-4 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 34
DSolve[{y''[x]+2*y'[x]-8*y[x]==8*x^2-3,{y[0]==1,y'[0]==-3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-4 x} \left (-2 e^{4 x} x (2 x+1)+e^{6 x}+3\right ) \]