60.1.3 problem 3

Internal problem ID [10017]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:18:22 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 35

DSolve[D[y[x],x] + a*y[x] - b*Sin[c*x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-a x} \left (\int _1^xb e^{a K[1]} \sin (c K[1])dK[1]+c_1\right ) \]