Internal problem ID [2198]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+P \left (x \right ) y=Q \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x)+P(x)*y(x)=Q(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\int Q \left (x \right ) {\mathrm e}^{\int P \left (x \right )d x}d x +c_{1} \right ) {\mathrm e}^{-\left (\int P \left (x \right )d x \right )} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 51
DSolve[y'[x]+p[x]*y[x]==q[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \exp \left (\int _1^x-p(K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-p(K[1])dK[1]\right ) q(K[2])dK[2]+c_1\right ) \]