Internal problem ID [9780]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1453.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-a^{2} y^{\prime }={\mathrm e}^{2 x a} \sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 124
dsolve(diff(diff(diff(y(x),x),x),x)-a^2*diff(y(x),x)-exp(2*a*x)*sin(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-9 a^{6}+36 a^{4}\right ) \cos \left (2 x \right )+\left (-33 a^{5}+12 a^{3}\right ) \sin \left (2 x \right )+9 a^{6}+49 a^{4}+56 a^{2}+16\right ) {\mathrm e}^{2 a x}+108 \left (a^{2}+\frac {4}{9}\right ) a^{2} \left (a^{2}+1\right ) \left (c_{3} a +c_{1} {\mathrm e}^{a x}-c_{2} {\mathrm e}^{-a x}\right ) \left (a^{2}+4\right )}{108 \left (a^{2}+\frac {4}{9}\right ) a^{3} \left (a^{2}+1\right ) \left (a^{2}+4\right )} \]
✓ Solution by Mathematica
Time used: 6.285 (sec). Leaf size: 128
DSolve[-(E^(2*a*x)*Sin[x]^2) - a^2*y'[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-a x} \left (-9 \left (a^2-4\right ) a^4 e^{3 a x} \cos (2 x)-3 \left (11 a^2-4\right ) a^3 e^{3 a x} \sin (2 x)+\left (9 a^6+49 a^4+56 a^2+16\right ) \left (12 a^2 c_1 e^{2 a x}-12 a^2 c_2+e^{3 a x}\right )\right )}{12 a^3 \left (9 a^6+49 a^4+56 a^2+16\right )}+c_3 \]