40.4.14 problem 19 (p)

Internal problem ID [6654]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (p)
Date solved : Monday, January 27, 2025 at 02:17:10 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

dsolve(x*diff(y(x),x)=y(x)*(1-x*tan(x))+x^2*cos(x),y(x), singsol=all)
 

\[ y = \left (x +c_1 \right ) \cos \left (x \right ) x \]

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 13

DSolve[x*D[y[x],x]==y[x]*(1-x*Tan[x])+x^2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x+c_1) \cos (x) \]