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x²(y-z)p + y²(z − x)q = z²(x-y)


Prove that Pn(1) = 1 and Pn(-1) = (-1)


Solve by method of variation of parameters, (D 4)y 4 tan2x


Particular integral of (D^2 +3DD' + 2D'^2) = 12xy

Evaluate

x^2y^3 + x(

1 + y^2)dy/dx= 0




Find the general solution and the second solution of,

x2y"-3xy'+4y=0,given y1(x)=x2



Solve (d^2y)/(dx^2)+y=sec^2x


1.y(3x^3-x+y)dx+x^2(1-x^2)dy=0
2.y(2x+y^2)dx+x(y^2-x)dy=0
1.y(3x^3-x+y)dx+x^2(1-x^2)dy=0
2.y(2x+y^2)dx+x(y^2-x)dy=0
Find the general integrals of the PDE

(Y+1)p+(x+1)q=z