Question

In: Advanced Math

Solve the initial value problem. y'=(y^2)+(2xy)+(x^2)-(1), y(0)=1

Solve the initial value problem. y'=(y^2)+(2xy)+(x^2)-(1), y(0)=1

Solutions

Expert Solution

Given initial value problem ,

  

or ,

or, ............

Let us make an substitution

Substituting these values in we get ,

Integrating both side we get ,

  

, where c is integration constant .

........

Since so ,

or ,

substituting value of in we get ,

or ,

Hence the required solution is ,

.

.

.

.

If you have any doubt or need more clarification at any step please comment .

Colby Messinger answered 3 years ago
Next > < Previous

Related Solutions

1) Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 3)...
1) Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 3) dy = 0,   y(1) = 1 2) Find the general solution of the given differential equation. x dy/dx + (4x + 1)y = e−4x y(x) = Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there are any transient terms in the general solution. (Enter the transient...
Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy...
Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0,   y(1) = 1
Solve the initial value problem: y''+2y'+y = x^2 , y(0)=0 , y'(0) = 0
Solve the initial value problem: y''+2y'+y = x^2 , y(0)=0 , y'(0) = 0
Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3...
Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3 y' being the first derivative of y(x), y'' being the second derivative, etc.
Solve the initial value problem (first state the type of the differential equation) y'(x) = (2xy)...
Solve the initial value problem (first state the type of the differential equation) y'(x) = (2xy) / (x^2−y^2) & y(1) = 1
Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it...
Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it analytically. (b) Solve it using Euler’s method using step size h = 0.1 and find an approximation to true solution at x = 0.3. (c) What is the error in the Euler’s method at x = 0.3
Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0)...
Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1, y'(0) = 0. Solve without the Laplace Transform, first, and then with the Laplace Transform.
Solve the following initial value problem. y(4) − 5y′′′ + 4y′′  =  x,    y(0)  =  0, y′(0)  ...
Solve the following initial value problem. y(4) − 5y′′′ + 4y′′  =  x,    y(0)  =  0, y′(0)  =  0, y′′(0)  =  0, y′′′(0)  =  0.
A) Solve the initial value problem: 8x−4y√(x^2+1) * dy/dx=0 y(0)=−8 y(x)= B)  Find the function y=y(x) (for...
A) Solve the initial value problem: 8x−4y√(x^2+1) * dy/dx=0 y(0)=−8 y(x)= B)  Find the function y=y(x) (for x>0 ) which satisfies the separable differential equation dy/dx=(10+16x)/xy^2 ; x>0 with the initial condition y(1)=2 y= C) Find the solution to the differential equation dy/dt=0.2(y−150) if y=30 when t=0 y=
1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value...
1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value problem. yy'=e^x+x , y(0)=y_0 y_0 is a nonzero constant.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT