1. State the order of the following differential equations. Which are linear and nonlinear? dy d²y dy а. dx + 2y2 = 0 e* + 1 d. dx dx² d²y e. 4 dx² d²y b. y + cos x = 0 dy + 3y = 3x + 2 dx2 dx d?y C. dx² – 9y = 0

Q: Which of the following is the transformed form of the 2y = x(y')³ – (v')² + 1 differential equation…

A: Given 2y=xy'3-y'2+1

Q: 4. For each of the following systems of differential equations, find the general solution and then…

A: Do mention that , as per our guidelines we are supposed to answer only? 3 sub- parts ( if there are…

Q: Determine the general solution of the following differential equation: (D²-2D+1)y = 35x(3/2) ex O A.…

A:

Q: The following are second order differential equations except. d' A. dy 3D10X dx dx B. dx +5x 7 d'y…

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Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A: Topic- homogeneous and linear differential equations

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given solution to a linear non-homogenous differential equation is    yt=c1et+c2e2t-3tet+cost-e-t2…

Q: the general solution to the second order linear differential equationd^2y/ dx^2 − 14dy/ dx + 51y =…

A: We will find the solution.

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is…

Q: Determine the particular solution of the first order linear differential equations dy + x[x2 – x +…

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Q: Solve the following differential equations of 2-x'y'y' + xy' = 1 x' +y 1- yy' = 2y – x; dy 3– 2xyy'…

A: To solve the given differential equation we use the substitution y=vx

Q: 45. The solution to the differential equation 3x dy - 2y dx = 4yx^3dy is O y^3 = x^3 y^2 + cx^3 O…

A:

Q: Which of the following is the general solution of the differential equation y (iv) +21y"-100y=0? O…

A: We will find out the required solution.

Q: 5. Solve the following simultaneous differential equations: dx dy (i) + 5x + y = et, x + 3y = e²t,…

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Q: What is the general solution to the differential equation 2ydx = (x² – 1)(dx – dy) ? 2y(x – 1) – x²…

A:

Q: Which of the following is the transformed form of the 2y = x(y')³ – (y')² +1 differential equation…

A: We have 2y=xy'3-y'2+1 Now , differentiate both sides with respect to x:…

Q: What is the general solution to the differential equation (x – 4y – 9)dx + (4x + y – 2)dy = 0 ? x-1…

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Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is…

A: We are given the solution as : y(t)=c1et+c2e2t-3tet+cos t-e-t2 ---(1)…

Q: Differential Equestion

A: Find the general solution as follows.The auxiliary equation of the given differential equation is,

Q: 1. State the order of the following differential equations. Which are linear and nonlinear? dy а. dx…

A: 1,a) The order of the differential equation is 1, it is linear. b) The order of the differential…

Q: Show that y = 3x et +e-3x is a solution of the differential equation y' + 3y = 3ex. 4 y = 2ex + e-3x…

A: Given the differential equation:

Q: Which of the following differential equation is non linear, second degree, dependent variable is y,…

A:

Q: 5. Find the general solution of the first-order linear differential equation. dy dx +7y 42 a. y = 7+…

A:

Q: Provide a step-by-step solution to the following differential equation (linear quation) y' = x3 -…

A: I am attaching image so that you understand each and every step.

Q: The following are nonhomogeneous linear differential equations except. A. 2xy" +x'y'-(sin x )y = 2…

A: For any function, y=f(x), x is the independent variable and y is the dependent variable. A linear…

Q: Determine the particular solution of the first order linear differential equations dy + x[x? – x +…

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Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A:

Q: 1. Solve the following linear differential equations: dy (a) + 3y 0 dx dy (b) -3y 0 dx d²y dy (c)…

A: The given differential equations are a)dydx+3y=0b)dydx-3y=0c)d2ydx2+2dydx+y=0d)d2ydx2-6dydx+9y=0

Q: 15. Determine the differential equation whose general solution is x= C,e" + C,te® . d²x dx – 36+12x…

A: We need to determine the ODE for which the solution is given in the question. This can be done as…

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A:

Q: Find the general solution of the given higher-order differential equation. d* y dx 7d -18y = 0 dx2 O…

A:

Q: The general solution of the given higher order differential equation of y" + 3y" - 4y =0is Oage*+…

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

Q: What is the differential equation corresponding to the general solution y= dy 3x A dx 2y dy _ 2y (B…

A:

Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A: Recall: Homogeneous Linear Equation with constant coefficients: An equation of the form…

Q: Find the general solution of the given higher-order differential equation. y(4) – 2y" + y = 0 Oy =…

A:

Q: 4. For each of the following systems of differential equations, find the general solution and then…

A: please see the next step for solution

Q: 2. ,Which of the following ordinary differential equation is equivalent to this first order system?…

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Q: Solve the following differential equations of 1- ye** . dy = dx; dy 2-- %3(1+ y*)e* dx m dy…

A:

Q: If yH of a differential equation is cje2* + cze3x + cze-3x, then W1 = %3D (a) 0 (b) 9 (c) 5e-* (d)…

A: If yH of a differential equation is c1e2x+c2e3x+c3e-3x, then we have to find the Wronskain W.

Q: Find a particular solution of the following differential equation dy e +2=x-3- dx satisfying initial…

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Q: Solve the following differential equations: 1. (r - y2) dx = 2xy dy 2. (x²y – 2xy?) dx - (r³ – 3x3y)…

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Q: Determine the particular solution of the first order linear differential equations dy x°(x + 4)…

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Q: 1. Identify the order, degree and linearity of the following differential equations: d²y 4 + 1]3 b)…

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

Q: (1-xy)^-2dx+[y^2+x^2(1-xy)^2]dy=0

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Q: Transform the differential equation xy" - 2y' + Axy = 0, into a Sturm-Linville differential equation…

A:

Q: Determine the solution of the differential equation 3(1+ t²) dy = 2ty(y³ – 1) dt а. 1 y-3 1+C(1+t?)…

A: Solution of differential equations

Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A: Differential equations are given, we have to find homogeneous linear differential equation with…

Q: Solve the given differential equation (2x – y + 2) dx + (6x – 3y+1) dy = 0 O 91z – 21y – 5 ln(14x –…

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Q: /hich of the following equations can be reduced to the homogenuous linear differential equation with…

A: The power of diffrenatiation and power of x should be same.   So a, b, c, d are discarded.

Q: ch of the following equations can be reduced to the homogenuous linear differential equation with…

A: We will check all the options for linear homogenous differential equation

Q: Find the general solution of the second order linear differential equationd^2y /dx^2 −dy/ dx − 12y =…

A: