29.2.10 problem 35

Internal problem ID [4643]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 35
Date solved : Monday, January 27, 2025 at 09:29:13 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 22

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

\begin{align*} y(x)\to c_1 e^{x (a+\sin (\log (x)))} \\ y(x)\to 0 \\ \end{align*}