47.5.12 problem 12

Internal problem ID [7501]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number : 12
Date solved : Monday, January 27, 2025 at 03:02:39 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=\left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \end{align*}

✗ Solution by Maple

dsolve((cos(x)-sin(x))*diff(y(x),x$2)-2*sin(x)*diff(y(x),x)+(cos(x)+sin(x))*y(x)=(cos(x)-sin(x))^2,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 15.357 (sec). Leaf size: 7186

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

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