y = C1 e2x c cos 3x + c2 e2* sin 3x

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

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Q: 4. 2ydx + (x ay³) dy = 0

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Q: 4. (y' — 5у) %3 х?е* — х е5x

A: According to question, Given differential equation, y'-5y = x2ex-xe5x.

Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: y' + y² = 3y tan x tan? x + 1

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Q: (e) If an initial condition of x(0) = 1, sketch the x(t) vs t graph. (f) Use the Euler method to…

A: We have to sketch the graph of the differential equation

Q: хdу — (у + х? сos(x)) dx — 0

A: First i have written the given differential equation into standard form of first order linearr…

Q: Determine whether the following equation is a solution to the corresponding differential equation.…

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Q: dy dy -4 =0 dx dx O 2 and 6 O 2 and 4 O 1 and 6 O 1 and 4

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Q: I (1-x) y"- 4xy't 5x = cos x 2 d + tx=0 3. to ylm) _ t° y" +6y = 0 4. x + Y =0 dx 5. x y' - 4 seny =…

A: Linear equation means independent variable is in linear. That is independent variable is free from…

Q: Solve the differential equation when = 5(10 – P) if P = 2 when t = 0.

A: Solving the problem by solving the diff equation.

Q: g. A thermometer reading 50°C is taken outside where the temperature is 30°C. Five minute later the…

A: Consider temperature of thermometer after 't' minutes is given by T(t), then from the given…

Q: 2) x – 1 = - 2e-y

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Q: 1.3x – xy = c -

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Q: y' = xcosecr + y cot r.

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Q: xdy – 4ydx = x®e*dx

A: A  differential equation is said to be linear if All the derivative and dependent variable is of…

Q: Write the differential equation for each of the curves determined by the given conditions. Find the…

A: Find the Differential equation of each curve.

Q: y" - g'+ J = 9 = cos x

A: step:-1 Given that y''' -y' +y =cos x --------(1) Take  v1=y  ---(1)v2=y' v3=y''   then ⇒ v1'=y' =v2…

Q: - y = c1x² + c2 e¬* .y = x2 + c1x + c2 e¯* D. y %3D ). у %3D Сте?x соs 3x + сz e2X sin Зx

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