04/19/23 Perkins

AP Calculus AB

Day 11Section 6.3

Solve the differential equation.

21.

1

dy xy

dx x

2

1

1

xdy dx

y x

2

1

1

xdy dx

y x

21u x

2du xdx21

2ln ln 1y x C 122ln ln 1y x C

12 2ln1ln x Cye e

12 2ln1 x Cy e e

1221y C x

0 1y 2. Given the initial condition , find the particular solution of the differential equation.

2

1 ' 0xxy e y y

2

1 0x dyxy e y

dx

2

1x dye y xy

dx

2

1xe y dy xydx 21 xy

dy xe dxy

21 xydy xe dx

y

211 xdy xe dxy

2u x

2du xdx1 1

12

udy e duy

12ln uy y e C

212ln xy y e C

20121 ln 1 e C

121 C

32 C

231

2 2ln xy y e

Perkins

AP Calculus AB

Day 11Section 6.3

Solve the differential equation.

21.

1

dy xy

dx x

0 1y 2. Given the initial condition , find the particular solution of the differential equation.

2

1 ' 0xxy e y y