29.15.5 problem 413

Internal problem ID [5011]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 413
Date solved : Monday, January 27, 2025 at 10:03:18 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

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

\[ y \left (x \right ) = c_{1} \left (-\cos \left (x \right )+\sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 20

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

\begin{align*} y(x)\to c_1 (\cos (x)-\sin (x)) \\ y(x)\to 0 \\ \end{align*}