Internal problem ID [2223]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime }={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
dsolve(diff(y(x),x$3)-diff(y(x),x)=exp(x)*(sin(x)-x^2),y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}-\frac {7 x \,{\mathrm e}^{x}}{4}+\frac {15 \,{\mathrm e}^{x}}{8}+\frac {3 \,{\mathrm e}^{x} x^{2}}{4}-\frac {x^{3} {\mathrm e}^{x}}{6}-\frac {{\mathrm e}^{x} \cos \left (x \right )}{10}-\frac {3 \,{\mathrm e}^{x} \sin \left (x \right )}{10}-{\mathrm e}^{-x} c_{2} +c_{3} \]
✓ Solution by Mathematica
Time used: 1.016 (sec). Leaf size: 63
DSolve[y'''[x]-y'[x]==Exp[x]*(Sin[x]-x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^x \left (-4 x^3+18 x^2-42 x+45\right )-\frac {3}{10} e^x \sin (x)-\frac {1}{10} e^x \cos (x)+c_1 e^x-c_2 e^{-x}+c_3 \]