77.1.117 problem 143 (page 213)

Internal problem ID [18007]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 143 (page 213)
Date solved : Tuesday, January 28, 2025 at 11:19:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)+p__1*diff(y(x),x)+p__2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {\left (-p_{1} +\sqrt {p_{1}^{2}-4 p_{2}}\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (p_{1} +\sqrt {p_{1}^{2}-4 p_{2}}\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]+p1*D[y[x],x]+p2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {1}{2} x \left (\sqrt {\text {p1}^2-4 \text {p2}}+\text {p1}\right )} \left (c_2 e^{x \sqrt {\text {p1}^2-4 \text {p2}}}+c_1\right ) \]