Internal problem ID [8653]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1073.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {\left (11 \WeierstrassP \left (x , a , b\right ) \WeierstrassPPrime \left (x , a , b\right )-6 \WeierstrassP \left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\WeierstrassPPrime \left (x , a , b\right )+\WeierstrassP \left (x , a , b\right )^{2}}+\frac {\left (\WeierstrassPPrime \left (x , a , b\right )^{2}-\WeierstrassP \left (x , a , b\right )^{2} \WeierstrassPPrime \left (x , a , b\right )-\WeierstrassP \left (x , a , b\right ) \left (6 \WeierstrassP \left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\WeierstrassPPrime \left (x , a , b\right )+\WeierstrassP \left (x , a , b\right )^{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)+(11*WeierstrassP(x,a,b)*WeierstrassPPrime(x,a,b)-6*WeierstrassP(x,a,b)^2+1/2*a)*diff(y(x),x)/(WeierstrassPPrime(x,a,b)+WeierstrassP(x,a,b)^2)+(WeierstrassPPrime(x,a,b)^2-WeierstrassP(x,a,b)^2*WeierstrassPPrime(x,a,b)-WeierstrassP(x,a,b)*(6*WeierstrassP(x,a,b)^2-1/2*a))*y(x)/(WeierstrassPPrime(x,a,b)+WeierstrassP(x,a,b)^2)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[((-(WeierstrassP[x, {a, b}]*(-1/2*a + 6*WeierstrassP[x, {a, b}]^2)) - WeierstrassP[x, {a, b}]^2*WeierstrassPPrime[x, {a, b}] + WeierstrassPPrime[x, {a, b}]^2)*y[x])/(WeierstrassP[x, {a, b}]^2 + WeierstrassPPrime[x, {a, b}]) + ((a/2 - 6*WeierstrassP[x, {a, b}]^2 + WeierstrassP[x, {a, b}]^3 - WeierstrassP[x, {a, b}]*WeierstrassPPrime[x, {a, b}])*y'[x])/(-WeierstrassP[x, {a, b}]^2 + WeierstrassPPrime[x, {a, b}]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved