4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP, ydx=x(y+1)dy &

4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP,

ydx=x(y+1)dy

y(e)=1

(b) Consider the IVP, test whether it is exact and solve it.

x(x-y)dy=-(3xy-y^2)dx

y(-1)=1

(c) Determine the degree of the following homogeneous function

(i) f(x,y)=4x^2+2y^4 ,

(ii) f(x,y)=√5x^6-3y^6+4x^2y^4 ,

Expert Solution

Colby Messinger answered 1 year ago

Solve IVP for y(x): dy/dx + (3/x)y = 8y^4, y(1) = 1

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4

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1) Let y be the solution of the equation y ′ = 4(x^4)*sin(x^4) satisfying the condition y ( 0 ) = − 1. Find y ( pi^1/3 ). 2) Find the largest value of the parameter r for which the function y = e^(rx) is a solution of the equation y ″ − 14 y ′ + 28 y = 0. 3) Let y ′ = − 4x^2*e^(-x^4) and let y ( 0 ) = 1. Find ln ⁡ (...

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Find dy/dx by implicit differentiation. 11. ycosx=x^2+y^2 13. sqrt(x+y)=x^4+y^4 15. tan(x/y)=x+y 17. sqrt(xy)=1+(x^2)*(y) 19. sin(xy) = cos(x+y)

Question

4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP, ydx=x(y+1)dy &

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