Internal problem ID [12471]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 7.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }=x \,{\mathrm e}^{x}-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 79
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+diff(y(x),x$2)=x*exp(x)-3*x^2,y(x), singsol=all)
\[ y \left (x \right ) = -26-9 x^{2}-\frac {x^{4}}{4}-2 x^{3}+y \left (0\right )+\frac {{\mathrm e}^{x} \left (x^{3}+6 x D^{\left (3\right )}\left (y \right )\left (0\right )-6 x D^{\left (2\right )}\left (y \right )\left (0\right )-6 x^{2}-12 D^{\left (3\right )}\left (y \right )\left (0\right )+18 D^{\left (2\right )}\left (y \right )\left (0\right )-18 x +156\right )}{6}-D^{\left (2\right )}\left (y \right )\left (0\right ) \left (3+2 x \right )+D^{\left (3\right )}\left (y \right )\left (0\right ) \left (x +2\right )+x \left (-23+D\left (y \right )\left (0\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.812 (sec). Leaf size: 59
DSolve[y''''[x]-2*y'''[x]+y''[x]==x*Exp[x]-3*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^4}{4}-2 x^3-9 x^2+e^x \left (\frac {x^3}{6}-x^2+(3+c_2) x-4+c_1-2 c_2\right )+c_4 x+c_3 \]