3. Solve the following Bernoulli's equations: (a) il (xxzy) 21 dy -5 dx +9y = y³e³2r

Q: Solve the Bernoulli Equation; dy/dx + 2y = exy-2

A:

Q: y³dx + (3xy¹) dy = 0 (6xy-y³¹) dx + (4y + 3x²-3xy²) oly =

A:

Q: b) Solve the following second order differential equation, clearly showing all calculation steps dy…

A: To solve the given second order differential equation :-

Q: solve using the appropriate method.

A:

Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: Write each equation in the form M(x) dx + N(x)dy = 0 test for exactness and solve those equations…

A:

Q: Find the solution to the Bernoulli equation: dy/dx + 2y/x = -x²y³

A: Introduction: One of the earliest differential equations to be solved was the Bernoulli equation,…

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: B. ty" – (t+ 1)y' + y = t?

A: Answer is mentioned below

Q: a) Solve the following first-order differential equations: dy = -y 2x, given that when y=0, x=+2 dx

A: We have given  -y dy/dx = 2x when y = 0 and x = +-2

Q: 4. Solve the following DE: (2x²y)y' = x³ + 2y³

A: Given in the question, The diffrential equation is as follows:- By dividing both sides by 2x2 * y3,…

Q: Determine the appropriate form for a particular solution of the fifth-order equation(D - 2)3 (D2 +…

A: Given differential equation is D−23D2+92y=x2e2x+xsin3x......1. We have to determine the appropriate…

Q: 4. Using homogenous D.E approach, solve (x³ – 3xy?)dx = (y3 – 3x²y)dy.

A:

Q: Solve the following equation for y(x): y" + 4y = 6 cos 3x + 20 sin 3x

A:

Q: a) Solve the following first-order differential equations: ER -y- = 2x, given that when y=0, x=+2

A: The given differential equation is:

Q: Solve the following D.E: 3. 9yy' + 4x = 0

A: Given a differential equation,9yy′+4x=0 , where y′=dydxyou have to the solve above differential…

Q: Solve  y′ + 2y cos(2t) = 2 cos(2t), y(π/2 ) = 0

A:

Q: Solve the following Bernoulli equation y' – y = (2t – 3)y i

A: Bernoulli Equation : Consider y'+p(x) y=q(x)ynThen we let v=y1-nAnd solve the equation by…

Q: I241 Solve the DE. (3x²y- xy)dx+(2r'y² +x*y*)dy = 0.

A:

Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: The solution of (xy – ) = y³e-x² dx

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: 2. Solve the following Bernoulli equation: xy' = y - xexy²

A: Given differential equation is    This can be written as      Substitute, , then we get   Thus,…

Q: Solve the initial value problem. (cosx)(dy/dx)+ysinx=6xcos2x, y(pi/3)=(-4pi2/3)

A:

Q: form.

A: The given differential equation is not exact .And the solution is:

Q: Describe two ways to find the general solution of (dy/dx) + 3xy = x. Verify that each method gives…

A: Given: The differential equation is dydx+3xy=x We have to find the general solution by two ways.

Q: Solve the DE. 2x²y' + 5xy – 35y = 0 — 0

A: