60.3.5 problem 1005

Internal problem ID [11015]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1005
Date solved : Monday, January 27, 2025 at 10:41:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 82

dsolve(diff(diff(y(x),x),x)+y(x)-sin(a*x)*sin(b*x)=0,y(x), singsol=all)
 

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\frac {-\left (b +a +1\right ) \left (b +a -1\right ) \cos \left (x \left (a -b \right )\right )+\cos \left (x \left (a +b \right )\right ) \left (-b +a +1\right ) \left (-b +a -1\right )}{2 a^{4}+\left (-4 b^{2}-4\right ) a^{2}+2 b^{4}-4 b^{2}+2} \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 65

DSolve[-(Sin[a*x]*Sin[b*x]) + y[x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x-\sin (K[1]) \sin (a K[1]) \sin (b K[1])dK[1]+\sin (x) \int _1^x\cos (K[2]) \sin (a K[2]) \sin (b K[2])dK[2]+c_1 \cos (x)+c_2 \sin (x) \]