►Solve the following differential equations 1. (x + 2y 2)dx + (2x − y + 3)dy = 0 [Answer: x² + 4xy - 4x - y² + 6y = c] 2.(2ax + by)ydx + (ax + 2by)xdy = 0 [Answer: ayx² + by²x = c]

Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

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Q: Solve the simultaneous equations 3 dx+y=z+ e* dz dx + z = y +et

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Q: Solve the given differential equation. dy = 18-ay %3! dx O y= (6x22 -C) O y = 6x2 + C O y = 6x + x2…

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Q: Solve the given equation.. dy - 3y = x³, v(1) = 10 X dx a. y(x)= x²Inx+5x³ b. v(x)= x?Inx + 10x³ c.…

A: Please refer to the image below

Q: Find the solution. (D-3D-2)y = 0 when x 0, y = 0 and y' 9, y" = 0 a. y = 2e- (3x-2)e* b. y 2ex+…

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Q: Q.4 Solve the differential equation . d*y d³y d²y dy + 4 dx* dx³ dx² dx

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Q: , solve this D using the differential operator (D - 13D2 + 36)y = 2e2x + 3e-2x + 4e3x + 5e-3x + 10e*

A: Using method of undetermined coefficients

Q: + y²(x+ 1)² = C

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Q: The solution of the differential equation dy dx 6. is 6x + C 6lnx + C | 4 6x + C 5 6lnx + C 2

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Q: 5x-y2 2xy+3y2" c. xy? - 2x5 + 3y³ = C d. xy? + x5 + y3 = C 29. Find the general solution in implicit…

A: We have to find solution of exact differential equation.

Q: 4- Solution of the following equation 4xy²dx + (x² + 1)dy = 0 is

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Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: Find the general solution to y = (1 – x)y² + (2x – 1)y – x. - Note that you can find an obvious…

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Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Solve the differential equation (D³ – D² – 4D+4) y = xe² +e3z

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Q: Find the general solution to y(4) – 6y " + 8y" = 0. In your answer, use c1, C2, C3 and c4 10 denote…

A: The detailed solution is as follows below:

Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: H.. Ext (x-1)dx +xdy=0 Ex² ( 2 √xy_y) dx-xdy=. 3 EX 2 27 2x² dy = x² + y² ax ५ +₁ Exh x dy-y dx Find…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: Solve for the differential equations. y = (2y – |dy x²y² + 1, \1+x?y2 + 2x ) dx

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Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: dy et + 4x Find if y = The answers have been slightly simplified. %3D dx 3x – 1 (3x – 1) (e² + 4) +3…

A: The given equation is y=ex+4x3x-1.

Q: Match the general solutions to the differential equations. (D²-18D+81)y=0 ✓ (D²+14D+49) y = 0 ✓…

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Q: Consider the equation (y² – 2x)dx + (2xy + 1)dy = 0. The general solution is ... xy² – x² + y =€ A…

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