Internal problem ID [2182]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }=\cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-4*diff(y(x),x)=cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-4 x} \left (\left (c_{3} -\frac {3 \cos \left (2 x \right )}{100}-\frac {\sin \left (2 x \right )}{25}-\frac {3}{100}\right ) {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{5 x}-\frac {c_{2}}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 41
DSolve[y'''[x]+3*y''[x]-4*y'[x]==Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{25} \sin (2 x)-\frac {3}{100} \cos (2 x)-\frac {1}{4} c_1 e^{-4 x}+c_2 e^x+c_3 \]