60.1.9 problem 9

Internal problem ID [10023]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:18:36 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y = c_{1} {\mathrm e}^{x \left (\sin \left (\ln \left (x \right )\right )+a \right )} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 32

DSolve[D[y[x],x] - (Sin[Log[x]] + Cos[Log[x]] +a)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x(a+\cos (\log (K[1]))+\sin (\log (K[1])))dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}