x' = -y – x(x² + y2)² y' = x – y(x2 + y2)², x(0) = (6, 0) %3D %3D

Q: Find f(x)

A: It is given that f'x=1+3x, f4=25.

Q: Differentiate. y = In [(x + 6)* (x + 7)® (x + 3)5] d [In [(x +6)*(x +7)® (x + 3)°]] = ] dx

A:

Q: (a) / (2.x4 + Vx3 + 4e* + + 8) dx - (b) / = x3 + 3x – 4 dx - x2 (c) (x + 4)(x³ – 9) dx .3 -

A:

Q: ' (x² +2)+4x(y² +2y+1)=0, y(0) =1.

A:

Q: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: In(t) Let y = %3D (a) ( Find y' using the quotient rule. (b) Rewrite y as a product, then find y'…

A: Given that y=lntt3. (a) Compute the derivative using quotient rule.…

Q: Let f(x) = (x° + 3x + 5) %3D f'(x) = %3D f'(3) =

A: We will solve by derivative

Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: f(x)= (x+2)² (x - 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

A:

Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: (15) y "'+ y " =e (16) y () – y (4) = 1 %3D

A:

Q: Solve: у" + 5у'" — 2y' - 24у — 42е 5t 2y' — 24у 3D 42e — 2, у'(0) — — 6, у'"(0) —D — 30 | | | y(t) =

A:

Q: . How we Can Solne it ? 2. *B" (K+t) Carzz) (a+3) KB (ati) (a+2) %3D

A: Some formulae's: (a+b)2=a2+b2+2ab Power addition: (xayb)(xcyd)=xa+cyb+d

Q: What's the limit function f(x) = lim fn(x),

A:

Q: f(x) = 8x-1 %3D f '(x) = %3D

A:

Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

A:

Q: Graph. -2x - 1 if x 1

A: The given function is f(x)=-2x-1;  if   x<-1        1    ;  if-1≤x≤1    2x-1;  if   x>1 Obtain…

Q: y' = {] 4-6 3-2 y, y(0) = 5 [5 2

A: y'=4-63-2yy0=52

Q: Let 4 f(x) = (a + 4x + 4)* f'(x) = f'(5) =

A:

Q: hat is y(t)?

A:

Q: (6x? - 6x +: -5x3 +9x+ 6 +5) h(x) %3D h'(x) = || %3D

A:

Q: f (x) = (x³ – 5x + 2)(x² + x – 7); find f'(x) %3D

A:

Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

A:

Q: If f' (2) = -5 and g'(2) = 3, find %3D (a) h'(2), if h(x) = 12f(x) + 4. %3D h' (2) = (b) F'(2), if…

A:

Q: 4- (x2 + y2 + x)dx + xydy = 0

A:

Q: xy y' = x² + y² %3D with y(1) = -4, then y(e)

A:

Q: y2+x2 5- y' %3D y(1) = -2 xy

A:

Q: Find f'(x). f(x) = (10x+ 7)' (1 – Va)° 6.

A: In this question we have to find the differentiation of the given function.

Q: If f(x) = x²/(1 + x), find f "(1). f"(1) = %3D %3D

A:

Q: If h(x) = f(x) – g°(x), f'(x) = -9(x) and g'(x) = f(x), then h'(x) is: %3D

A: The solution of the problem is given in the next step.

Q: If g(x) = f(x² + 9x) and f'(10) = 3 , %3D %3D then g'(1) = (A) 11 (B) 3 (C) 33 (D) 29 (E) 87 (A) (B)

A:

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

A:

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.