73.3.2 problem 4.3 (b)

Internal problem ID [15036]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.3 (b)
Date solved : Tuesday, January 28, 2025 at 07:28:11 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=3 x -y \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x)=3*x-y(x)*sin(x),y(x), singsol=all)
 

\[ y = \left (3 \left (\int x \,{\mathrm e}^{-\cos \left (x \right )}d x \right )+c_{1} \right ) {\mathrm e}^{\cos \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 51

DSolve[D[y[x],x]==3*x-y[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x-\sin (K[1])dK[1]\right ) \left (\int _1^x3 \exp \left (-\int _1^{K[2]}-\sin (K[1])dK[1]\right ) K[2]dK[2]+c_1\right ) \]