7.4.32 problem 31 (b)

Internal problem ID [104]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 31 (b)
Date solved : Friday, February 07, 2025 at 07:49:32 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x)+p(x)*y(x)=q(x),y(x), singsol=all)
 

\[ y = \left (\int q \left (x \right ) {\mathrm e}^{\int p \left (x \right )d x}d x +c_1 \right ) {\mathrm e}^{-\int p \left (x \right )d x} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 51

DSolve[D[y[x],x]+p[x]*y[x]==q[x],y[x],x,IncludeSingularSolutions -> True]
 

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