15.12.25 problem 25

Internal problem ID [3169]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:24:51 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.037 (sec). Leaf size: 51

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

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