Internal problem ID [12777]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number: 4.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }=6 x -20-120 x^{2} {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)=6*x-20-120*x^2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-2 x^{5}+10 x^{4}-40 x^{3}+\left (c_{3} +120\right ) x^{2}+\left (c_{2} -2 c_{3} -240\right ) x +c_{1} -c_{2} +2 c_{3} +240\right ) {\mathrm e}^{x}-3 x^{2}+2 x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.569 (sec). Leaf size: 65
DSolve[y''''[x]-3*y'''[x]+3*y''[x]-y'[x]==6*x-20-120*x^2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -3 x^2+e^x \left (-2 x^5+10 x^4-40 x^3+(120+c_3) x^2+(-240+c_2-2 c_3) x+240+c_1-c_2+2 c_3\right )+2 x+c_4 \]