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Solve the differential equation by substitution suggested by equation. Show complete solution.
(dy/dx) = 2y/x + cos(y/x2)
Obtain the general solution of the following differential equations.
1. ππ¦ + π¦πxππ₯ = πxππ₯
2. π₯ππ¦ = (πx β 2π¦)ππ₯
Obtain the particular solution satisfying the indicated conditions.
3. (2π¦ β π₯3)ππ₯ = π₯ππ¦, π¦(2) = 4
Obtain the general solution of the following equations.
1. (4π₯π¦ + 3π¦2 )ππ₯ + π₯(π₯ + 2π¦)ππ¦ = 0
2. (3π₯3 + π¦2 )ππ₯ β 2π₯π¦ππ¦ = 0
Obtain the particular solution satisfying the indicated conditions.
3. (4π₯3 β 3π¦2 )ππ₯ + 6π₯π¦ππ¦ = 0, π¦(β1) = 0
determine the exactness and obtain the general solutions.
1. (π₯ + π¦2 )ππ₯ + (2π₯π¦ + π¦2)ππ¦ = 0
2. (2π₯π¦3 + π₯2 )ππ₯ + (3π₯2π¦2 + π¦)ππ¦ = 0
3. (π2y + π₯)ππ₯ + (2π₯π2y + 1)ππ¦ = 0Β
Ut(x,t)=10Uxx(x,t) -10
U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0
Ux(x,0)=x+1 -1
Solve the following initial value problem
Ut(x,t)=10Uxx(x,t) -10
U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0
Ux(x,0)=x+1 -1
(1+x)dy/dx-xy=x+x^2
Β Find the eigenvalues and eigenfunctions of the following Sturm-Liouville probelm (e^(2x)y')' + e^(2x) (Ξ» + 1)y = 0; y(0) = 0 = y(Ο).Β
Β Evaluate (π«π + ππ« + π)π = π βππ β ππππππ + πππ5
Solve the following IVP by power series method
xyβ²β² + yβ² + 2y = 0, y(1) = 2,yβ²(1) = 4.
