50.1.67 problem 67

Internal problem ID [10065]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 67
Date solved : Tuesday, September 30, 2025 at 06:51:55 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 3 y y^{\prime \prime }+y&=5 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 59

ode:=3*y(x)*diff(diff(y(x),x),x)+y(x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} -3 \int _{}^{y}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_1 -6 \textit {\_a}}}d \textit {\_a} -x -c_2 &= 0 \\ 3 \int _{}^{y}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_1 -6 \textit {\_a}}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 41

ode=3*y[x]*D[y[x],{x,2}]+y[x]==5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2}{3} (5 \log (K[1])-K[1])}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]

✓ Sympy. Time used: 165.567 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), (x, 2)) + y(x) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ \sqrt {3} \int \limits ^{y{\left (x \right )}} \frac {1}{\sqrt {- 2 u + C_{1} + 10 \log {\left (u \right )}}}\, du = C_{2} + x, \ \sqrt {3} \int \limits ^{y{\left (x \right )}} \frac {1}{\sqrt {- 2 u + C_{1} + 10 \log {\left (u \right )}}}\, du = C_{2} - x\right ] \]