Differential Equations Answers

1.At 1:00 P.M., a thermometer reading 70°F is taken outside where the air temperature is -10°F. At 1:02 P.M., the reading is 26°F. At 1:05 P.M., the thermometer is taken back indoors, where the air is at 70°F. What is the temperature reading at 1:09 P.M.?

Coefficients linear in two variables

(3x − y + 2) dx + (9x − 3y + 1)dy = 0

Bernoulli’s Equation

(y^4 − 2xy)dx + 3x^2 dy = 0 when y(1)=0

Substitution as suggested by the equation

sinxsinydx + cosxcosydy = 0

Substitution as suggested by the equation

(x + 2y − 1)dx + 3(x + 2y)dy = 0 when y(0) = 2

Integrating factors found by inspection

y(x^2 y^2 − 1)dx + x(x^2 y^2 + 1)dy = 0

Integrating factors found by inspection

y(x^2 + y^2 − 1)dx + x(x^2 + y^2 + 1)dy = 0 when y(1) = 0

Use method of undetermined coefficients method to solve the following

y''+y=5xsinx,y(0)=0,y'(0)=1

Form the PDE of the following by eliminating arbitrary functions

phi(z^2-xy,x/z)

Solve the PDE whose auxiliary equations as follows: 𝑑𝑥/ 2𝑦(𝑧 − 3) = 𝑑𝑦 /𝑦(2𝑥 − 𝑧) = 𝑑𝑧 /𝑦(2𝑥 − 3)