# Revision history [back]

### Differential system of equations in Sage

Greetings all!

This is a "how do I do it in Sage" question. Let's say I have the following system of differential equations: (a, b, p, r, and h are ALL functions of t) eqn1 = diff(a,t) == 3p eqn2 = diff(b,t) == 4 + r eqn3 = h == a^2 + b^2 NOW, I want to differentiate h from equation three (using implicit differentiation). The "answer" would be: diff(h,t) = 2adiff(a,t) + 2b*diff(b,t) (note that we DO know what diff(a,t) and diff(b,t) are from eqn1 and eqn2) --> How can I get sage to differentiate eqn3, AND plug in the equations from eqn1 and eqn2 for the time derivatives of a and b?

### Differential system of equations in Sage

Greetings all!

This is a "how do I do it in Sage" question. Let's say I have the following system of differential equations: equations:

(a, b, p, r, and h are ALL functions of t) t)

eqn1 = diff(a,t) == 3p 3*p

eqn2 = diff(b,t) == 4 + r r

eqn3 = h == a^2 + b^2 b^2

NOW, I want to differentiate h from equation three (using implicit differentiation). differentiation).

The "answer" would be: diff(h,t) = 2aadiff(a,t) + 2bb*diff(b,t) diff(b,t) (note that we DO know what diff(a,t) and diff(b,t) are from eqn1 and eqn2)

--> How can I get sage to differentiate eqn3, AND plug in the equations from eqn1 and eqn2 for the time derivatives of a and b?

### Differential system of equations in Sage

Greetings all!

This is a "how do I do it in Sage" question. Let's say I have the following system of differential equations:

(a, b, p, r, and h are ALL functions of t)

eqn1 = diff(a,t) == 3*p

eqn2 = diff(b,t) == 4 + r

eqn3 = h == a^2 + b^2

NOW, I want to differentiate h from equation three (using implicit differentiation).

The "answer" would be: diff(h,t) = 2a2 * a * diff(a,t) + 2b2 * b * diff(b,t) (note that we DO know what diff(a,t) and diff(b,t) are from eqn1 and eqn2)

--> How can I get sage to differentiate eqn3, AND plug in the equations from eqn1 and eqn2 for the time derivatives of a and b?

### Differential system of equations in Sage

Greetings all!

This is a "how do I do it in Sage" question. Let's say I have the following system of differential equations:

(a, b, p, r, and h are ALL functions of t)

eqn1 = diff(a,t) == 3*p

eqn2 = diff(b,t) == 4 + r

eqn3 = h == a^2 + b^2

NOW, I want to differentiate h from equation three (using implicit differentiation).

The "answer" would be: diff(h,t) = 2 * a * diff(a,t) + 2 * b * diff(b,t) (note that we DO know what diff(a,t) and diff(b,t) are from eqn1 and eqn2)

--> How can I get sage to differentiate eqn3, AND plug in the equations from eqn1 and eqn2 for the time derivatives of a and b?