Internal problem ID [9787]
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]]
\[ \boxed {y^{\prime \prime \prime }-a^{2} y^{\prime }={\mathrm e}^{2 a x} \sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 234
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)
\[ y \left (x \right ) = \frac {108 \,{\mathrm e}^{a x} c_{1} a^{8}-108 \,{\mathrm e}^{-a x} c_{2} a^{8}+108 c_{3} a^{9}+588 \,{\mathrm e}^{a x} c_{1} a^{6}-588 \,{\mathrm e}^{-a x} c_{2} a^{6}-9 \cos \left (2 x \right ) {\mathrm e}^{2 a x} a^{6}+588 c_{3} a^{7}-33 \sin \left (2 x \right ) {\mathrm e}^{2 a x} a^{5}+9 \,{\mathrm e}^{2 a x} a^{6}+672 \,{\mathrm e}^{a x} c_{1} a^{4}-672 \,{\mathrm e}^{-a x} c_{2} a^{4}+36 \cos \left (2 x \right ) {\mathrm e}^{2 a x} a^{4}+672 c_{3} a^{5}+12 \sin \left (2 x \right ) {\mathrm e}^{2 a x} a^{3}+49 \,{\mathrm e}^{2 a x} a^{4}+192 \,{\mathrm e}^{a x} c_{1} a^{2}-192 \,{\mathrm e}^{-a x} c_{2} a^{2}+192 c_{3} a^{3}+56 \,{\mathrm e}^{2 a x} a^{2}+16 \,{\mathrm e}^{2 a x}}{12 a^{3} \left (9 a^{2}+4\right ) \left (a^{2}+4\right ) \left (a^{2}+1\right )} \]
✓ 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]
\[ y(x)\to \frac {e^{-a x} \left (-9 \left (a^2-4\right ) a^4 e^{3 a x} \cos (2 x)-3 \left (11 a^2-4\right ) a^3 e^{3 a x} \sin (2 x)+\left (9 a^6+49 a^4+56 a^2+16\right ) \left (12 a^2 c_1 e^{2 a x}-12 a^2 c_2+e^{3 a x}\right )\right )}{12 a^3 \left (9 a^6+49 a^4+56 a^2+16\right )}+c_3 \]