Internal problem ID [13300]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\sin \left (x \right ) y=3 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)=3*x-y(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (3 \left (\int x \,{\mathrm e}^{-\cos \left (x \right )}d x \right )+c_{1} \right ) {\mathrm e}^{\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.785 (sec). Leaf size: 31
DSolve[y'[x]==3*x-y[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\cos (x)} \left (\int _1^x3 e^{-\cos (K[1])} K[1]dK[1]+c_1\right ) \]