a z 8. 5. Solve the given partial differential equation

Q: 5) y=cixl+c2x+c3xlnx +4x? x'y"'+2x'y"-xy'+y=12x=

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Q: The differential equation xdy - ydx = 1 B. X A. 2x³ dx can be made exact by using what integrating…

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Q: (y² + 2xy)dx + x²dy = 0 2.

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Q: (x + 1) + y = lnx, y(1) = 10 dy dx

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Q: 11. (2х — бу + 4)dx + (х — 2у — 3)dy — 0; when x — 1, у %3 1

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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: • / = Ity

A: y'=x-yx+y It is a homogeneous differential equation. Put, y=vx⇒y'=v+x·dvdx Therefore,…

Q: (2xy + x)dy – [x² + y² + y + 1]dx = 0 When:x = 1; y = 0

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Q: 6. 7. 8. 9. 10. yy" = x аги аги аги + дх2 ' дуг ' дz2 d'y dx4 = w(x) d²y d²x -y dt² dt² di L+Ri= E…

A: We have to find the given differential equation is ordinary differential equation or partial…

Q: The differential equation dP = 10-4 P(318-1.7P) dt models the growth of the United States population…

A: The population of united states is given by, dPdt=10−4P318−1.7P Here P is in million and t is the…

Q: 2) y = c1e5x + cze²2×.-ex : y"-3y'-10y=6ex 2

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Q: Q5.5 Working from first principles develop the 1st order differential equation that describes a two…

A: Let Q be the inflow rate to the pump. Suppose, Qa be the stored volume per unit time in the pump and…

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: 10. (2ху*eУ + 2хуз + у) dх + (x?y*eУ — х?у?— 3х) dy — 0; when x - -1, у — 1

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Q: a. b. d²y dt² d²y dt² +4y= cos2t y(0)=-2 and y'(0) = 0 dy + 5y = 2ety(0) = 3 and y'(0) = 1 dt

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Q: (xy + y ln y)dx + (xy + x In x)dy = 0; when x = 1, y = 1

A: 7. The given differential equation is  (xy + y ln(y))  dx + (xy + x ln(x )) dy= 0   ....(1) with…

Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: 5.Solve the linear differential equation for general solution

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Q: A certain virus is known to spread among a population at a rate proportional to the fraction of the…

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Q: d*y Obtain a particular solution for dx+ d²y + + dx² * + y = x³ + 2x + 1 dx

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Q: 9. 10. d²y d²x dt² -y di L=+Ri= E dt dt² = C₁

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Q: (D² + 1) y = x cos x

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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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.