2. Find the explicit general solution to the given differential equation. Hint: Separable DE 3x=y² + x³y' = 2y²

Q: 1. Find the general solution of each of the differential equation y" – 2y' +y = 0.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 10. Find the general solution of the first-order linear differential equation. dy dr y = el 10x

A:

Q: (b) Without solving. What is the form of a particular solution of the given differential equation y"…

A:

Q: 1. Obtain the solution of the following differential equations: y'=Yly-2) x(y-1) а.

A:

Q: Find the general explicit solution to the differential equation xyy′ = x2 + 1

A: The given differential equation is xyy'=x2+1 We have to find the general explicit solution of the…

Q: Find the general solution of the given second-order differential equation. 3y" + y' = 0 y(x) =

A: Given second order differential equation is 3y"+y'=0.

Q: determine the general solution of the given differential equation.  y(4) − 4y″ = t2 + et

A:

Q: 1. Use the method of homogenous equations to solve the following differential equation (2² + 3y²)dx…

A: We use the method of homogeneous equations to solve the given question.

Q: 1. Describe the solution of the differential equation ydx – 2xy dy = 0.

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Q: Find the general solution to the following Cauchy-Euler differential equation 2 x²y" + xy + 4y = 2x…

A: To Solve: The differential equation x2y''+xy'+4y=2xlnx.

Q: Find the General Solution of the given exact differential equation. dy (8x + 7) + 2y= x da

A: We have to find the general solution of the given differential equation

Q: It is known that y = ekt is a solution of the differential equation y″ − 16y = 0. Find the value(s)…

A: Given that,

Q: Find the general solution of the given second-order differential equation. y" + 36y = 0 y(x)

A:

Q: 4. Find the general solution of the differential equation using the method of undetermined…

A: Let's find.

Q: Solve the given differential equation. (Hint: Bernoulli) y +y = y2

A: As we know that, the standard form of the linear differential equation. dydx+py=Q Where; ''p'' &…

Q: 1.) + y = 0 dx

A: Ony 1first question

Q: 6. Find the particular solution to the differential equation: (y +2)y"=3x*y+4y, given: y(0) = 1…

A:

Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: Find the general solution of the given second-order differential equation. y" + 16y = 0 %3D y(x) =

A: We have to find

Q: 1. Solve (explicitly) the separable Differential Equation du = + with y(0) = 2. y?+1 y(x+1)

A: Given differential equation is first order variables separable differential equation. we have also…

Q: dy dx + y = 2xy-ex

A:

Q: y' + (1+ 2x2) .e²²+y = 0

A:

Q: 1.Assess if the equation is homogeneous, then find the solution to the following differential…

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Q: Obtain the general solution of the given differential equation: dy = cos²xcosydx

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Q: What value of k would make the differential equation dy + In(x+1) = a'yk variables separable? O 2 O…

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Q: The particular solution of the following nonhomogeneous differential equation y" - 2y' +y = x? + e*…

A: To find  The particular solutions of the given differential equations

Q: (5) Find the solution of the following separable differential equation: dy -x(y + 2)², y(0) = 2. dx

A:

Q: Given a differential equation dy +y ln x = x*e* dx with an initial condition y(1)= 0. If the value…

A:

Q: 1. Find the general solution to the differential equation dy 1 - dx

A: Find your answer below

Q: Find the general solution of the given second-order differential equation. y" + 4y = 0 y(x) =

A:

Q: Solve the given differential equation. (Hint: Bernoulli) y' + y = y?

A:

Q: The particular solution of the following nonhomogeneous differential equation y" - 2y' +y = 4x? + e*…

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

Q: 5. Find the general solution of the given second order differential equation: y" + 8y' + 16y = 0

A:

Q: Find the general solution of the given second-order differential equation. 3y"+y' = 0 y(x) = =

A: To find out the general solution of the given differential equation.

Q: 1.Assess if the equation is homogeneous, then find the solution to the following differential…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5. Find the general solution of the following separable differential equation (e +4y²)=9xe* dx

A:

Q: :) x(x² + 1 )y' + 2y = ( x² + 1 )

A:

Q: Find the general solution of the given second-order differential equation. 3y" + y = 0 y(x) = ||

A: We have to find the general solution of given second order differential equation

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: what is the particular solution to the differential equation dy/dx=2cos(x)(y+1) with the initial…

A: We will integrate using the separation of variables method. Then we will evaluate the constant using…

Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…

A:

Q: 7. Find the general solution of the following differential equation: V1 + x²dy – xydx = 0.

A: Explanation of the answer is as follows

Q: Find the particular solution of the following differential equation: y'= ky(1-y), y(0)=-1

A:

Q: 3) ( y³ + × )V = 1 x (2) = 1

A: In the given problem initial conditions was wrong it should be y(2) =1 instead of x(2) =1, since 'y'…

Q: Given the differential equation y' – 2y = e2x with Initial Condition y(0) = 2, which of the…

A: I have given the answer in Step-2.

Q: . Find the explicit general solution to the given differential equation. Hint: Linear DE. (2x + 1)y'…

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Q: 6. xy' +y-x+ xycotx = 0

A:

Q: Find the general solution of the given higher-order differential equation. у" + 3y" + 3y' + y = 0…

A:

Q: 2. Determine the general solution of the given Differential Equation (x2 – xy + y?)dx – xydy = 0 - -

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Q: 4. 2ydx + (x x³y³) dy = 0

A: Here we have to solve the given differential equation