Solve the given problem on Linear Equations of Order One specifically on of (3xy + y)dx – y?dy = 0 the Separation Variables.

Q: 2. (a) Prove that the substitution u = yl¬n reduces the Bemoulli's equation + P(x)y = f(x)y", n ± 0…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the non-homogeneous equation of the 2md order D.E. y + ỹ– 2y = -5x³ + 2x mogeneous equation of…

A:

Q: 1. Determine the general solution of the following nonhomogeneous linear equations. dy 1. dx ex 2+ y…

A: Second order linear non−homogeneous differential equation with constant coefficients A second order…

Q: Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dB %3D 5 t y(1) = 2

A: Given: dy=3-y5-tdt+dBt y1=2 We have to apply Euler-Maruyama method as one step to solve the SDE.

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x+ y²)dx…

A:

Q: Using the substitution x = X and y = Y – 1, show that the equation dy x -у— 1 dx x + y+ 1 can be…

A:

Q: Obtain the general solution to the equation. (6t + 2y + 3)dt – dy =0 The general solution is y(t) =…

A:

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

A:

Q: Find an integrating factor and solve: y²dx + (3xy + y² – 1)dy = 0

A:

Q: Find the general solution of dy – qy³ Py – dt by making a suitable substitution that transforms the…

A:

Q: 5. Solve the unknown function 2 = ay (1 – by) dx 6. Given y(0) = ½, solve = 3x?y2. 7. Derive the…

A:

Q: Solve the given system of differential equation by laplace transformation dx —х - у di dy 5х — у. dt…

A:

Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

A:

Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

A:

Q: Find the equilibrium solutions for dy = -2 + 3y – yʻ dt .2

A:

Q: Find the general solution of dy xy = 1+ y?

A:

Q: B. Determine the general solution of the following nonhomogeneous linear equations using the method…

A:

Q: Obtain the general solution to the equation. (3t + 4y + 2)dt – dy = 0 The general solution is y(t)…

A:

Q: Solve the given initial-value problem. dx = -11x - y dt dy 3D 25х — у dt x(1) = 0, y(1) = 1 %3D x(t)…

A:

Q: Obtain the general solution to the equation. (5t + 5y + 2)dt – dy = 0 The general solution is y(t) =…

A:

Q: In the process of finding the orthogonal trajectories, a student determined that the differential…

A:

Q: Use the Euler method to solve d²y 0.5t + y = 0 dt2 where y (0) = 2 and y'(0) = 0. Solve from x = 0…

A:

Q: Find the equilibrium solutions of  dy/dx=2y(y-2), and based on the direction field, determine the…

A: Below is the solution:-

Q: The method used in solving the first order Bernoulli's equation dy ay +b (x) y=c(x) y" dx where n#0,…

A: We have to find the differential equation

Q: Solve the given initial-value problem. dy 3D х+ 4y, у(0) %3D 6 dx y(x) =

A: Given that dydx=x+4y , and y(0)=6We need to find the solution of above differential equation.

Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? А)…

A: Find orthogonal trajectory

Q: Find a general solution to the given Cauchy-Euler equation for t>0. dy + 2t- - 20y = 0 dr? dt The…

A:

Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

A:

Q: Find the general solution of d²y x(x +2) dy + (x + 2)y(x) = x³, dx dx? given that y, (x) = x and…

A: The given differential equation is solving through the variation of parameters below.

Q: Q5: Find the general solution of d²y + 4y = 3 cos 2t, y(0) = 2, (0) = 1. dt %3D %3D dt2

A:

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: solution :-

Q: Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

A:

Q: Find general solution of (x − 4y − 3)dx + (−x + 6y + 5)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

A:

Q: Find the general solution of d²y x(x + 2) dx² dy + (x + 2)y(x) = x³, dx given that y, (x) = x and…

A:

Q: 3. y'(x'y-2)dx+x(x*y' + 2y° - x)dy = 0 : y(1) = 1

A: We have to find the particular solution.

Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dy +31- 63y 0 dt dr?

A:

Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

A:

Q: Find a particular solution to the ODE: y"+ y' – 2y = e* cos(2t) Yp(t) =

A: Given:  y''+y'-2y=e2t cos2t To Find:  To find the particular solution to the given ODE.ypt=?

Q: Use the method of separable equations to solve the following initial value problems. dx/dt=…

A: It is given that dx/dt=xsin(t) with initial condition x(0) =1 and xy′=y2 with initial condition y(1)…

Q: Solve the given initial value problem. dx = 3x + y- e 3t, x(0) = 1 %3D dt dy = 4x + 3y, dt У(0) - -…

A:

Q: Obtain the general solution to the equation.   (2t+y+5)dt−dy=0

A:

Q: Solve the given initial-value problem. dx = -7x – y dt dy — 9х — у dt x(1) %3D 0, у(1) 3D 1 x(t) %D…

A: Given dxdt = -7x - y      ---(1)dydt = 9x - y        ---(2)with x(1) = 0, y(1) = 1

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

A:

Q: Solve the given initial-value problem dr At = 3x + y – e", r(0) = 3, dt %3D dy 2x + 4y, y(0) = -4.…

A: Step:-1 Given system of differential equation is dxdt=3x+y-e4t,   x(0)=3dydt=2x+4y,   y(0)=-4 Take…

Q: 4. Find the solution of the following set of simultaneous equations by ' conditions y(0) = x(0) = 0…

A: