(e) Second order differential equation 3. The nontrivial analytical solution of (a) 3-et dx x + dt (b) 3+e (c) 3+e x = with x(0) = 4 is (d) -3 + e* (e)-3-e

Q: Given, (- + 4) dx + (4ª+1) dy = 0 is an exact differential equation. x2 y4 Determine the value of A.

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Q: What is the general solution of an EXACT DIFFERENTIAL EQUATION? * A. g(y) + u(x,y) + C B. f(x) +…

A: To write the general solution of an exact differential equation.

Q: (c) Determine whether the equations below is a linear differential equation or not. Briefly explain…

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Q: (x² + b²)dy = 2x[(x² + b?)² + 3y]dx; y(b) = 4b*;

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Q: 6. Solve the initial value problem (2y3 – x³)dx + 3xy?dy = 0, y(1) = 1 a. 5y3x? = x5 + 4 c. 5y3x? =…

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Q: Exercise (2): Determine whether the differential equation is linear or nonlinear: (1) (1- )y" - 4ry…

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Q: Given a differential equation (6+ x²) +2.xy = (6 + x² k* dx (a) Solve the differential equation. (b)…

A: In the given question we have to solve the given differential equation. The given differential is…

Q: Q8. If f(t) = 2u(t-1)-3u(t-4) (a) 4 (b) 1 (c) 00 + 8(t-1)+2, then f(2)= (d) -1 (e) None of the above

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Q: (x + 2y) dx + (2x + y) dy = 0. ANS. x² + 4xy + y² = c.

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Q: What is the general real solution of the differential equation x3) – x(1} - 2x = 0 (the given…

A: The solution of linear homogeneous differential equation is defined by the roots of its…

Q: Q-28 Solve the differential equation (D – 6D+9)y=e³z(x+2) %3D

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Q: erential equation of a physical system satisfies the followin dP a =ag - bP dt

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Q: y0.5 + y15 = 1; y(0) = 4 dx

A: Given equation is y0.5dy/dx +y1.5=1 and y(0)=4

Q: solve differential equation y´+2y=4x y(0)=0

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Q: (1 point) The solution of a certain differential equation is of the form y(t) = a exp(7t) +…

A: We ae given : y(t)=a exp(7t)+b exp(10t) ⇒y(t)=ae7t+be10t We are given y(0)=4 ⇒4=a+b --(1) Now,…

Q: Q7. The indicial equation for x²y" - 3xy' + (4-x²) y = 0 is (a) r²- 2r + 4 = 0 (b) (r - 2)² = 0 (d)…

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Q: dy dx + x³ 3 The value of

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Q: 1. Find all singular points of the following differential equations. Classify them as regular…

A: Find all singular points of the following differential equations. Classify them as regular singular…

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Q: (1) The general solution of the ordinary differential equation (p- x)(p – y) = 0 , (p = ) is (a) (2y…

A: We need to find the general solution of p-xp-y=0 , where p=dydx We have p-xp-y=0 Just equating both…

Q: 4. Find the general solution of 2x³y' = y(y2 + 3x2) y²(C- x) = x3 b. y?(C + x) = x c. y?(C- x) = -x…

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