FirstOrder - Maple Help

Student[ODEs][Solve]

 FirstOrder
 Solve a first order ODE

 Calling Sequence FirstOrder(ODE, y(x))

Parameters

 ODE - a first order ordinary differential equation y - name; the dependent variable x - name; the independent variable

Description

 • The FirstOrder(ODE, y(x)) command finds the solution of a first order ODE.
 • Use the option output=steps to make this command return an annotated step-by-step solution.  Further control over the format and display of the step-by-step solution is available using the options described in Student:-Basics:-OutputStepsRecord.  The options supported by that command can be passed to this one.

Examples

 > $\mathrm{with}\left({{\mathrm{Student}}_{\mathrm{ODEs}}}_{\mathrm{Solve}}\right):$
 > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)=0$
 ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
 > $\mathrm{FirstOrder}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{{{z}{}\left({t}\right)}^{{2}}}{{2}}{-}{z}{}\left({t}\right){+}{\mathrm{ln}}{}\left({z}{}\left({t}\right){+}{1}\right){=}{-}\frac{{{t}}^{{2}}}{{2}}{-}{t}{-}{\mathrm{ln}}{}\left({t}{-}{1}\right){+}{\mathrm{_C1}}$ (2)

Compatibility

 • The Student[ODEs][Solve][FirstOrder] command was introduced in Maple 2021.
 • The Student[ODEs][Solve][FirstOrder] command was updated in Maple 2022.
 • The output option was introduced in Maple 2022.
The text passage describes a Maple command for solving first-order ordinary differential equations (ODEs) and provides an example of its usage.
no_question

the passage does not contain a mathematical question that requires an answer. it is a description of a maple command and an example of how to use it. the example shows the command being used to solve a specific ode, but it is presented as an illustration rather than a question to be answered.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
FirstOrder - Maple Help

Student[ODEs][Solve]

 FirstOrder
 Solve a first order ODE

 Calling Sequence FirstOrder(ODE, y(x))

Parameters

 ODE - a first order ordinary differential equation y - name; the dependent variable x - name; the independent variable

Description

 • The FirstOrder(ODE, y(x)) command finds the solution of a first order ODE.
 • Use the option output=steps to make this command return an annotated step-by-step solution.  Further control over the format and display of the step-by-step solution is available using the options described in Student:-Basics:-OutputStepsRecord.  The options supported by that command can be passed to this one.

Examples

 > $\mathrm{with}\left({{\mathrm{Student}}_{\mathrm{ODEs}}}_{\mathrm{Solve}}\right):$
 > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)=0$
 ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
 > $\mathrm{FirstOrder}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{{{z}{}\left({t}\right)}^{{2}}}{{2}}{-}{z}{}\left({t}\right){+}{\mathrm{ln}}{}\left({z}{}\left({t}\right){+}{1}\right){=}{-}\frac{{{t}}^{{2}}}{{2}}{-}{t}{-}{\mathrm{ln}}{}\left({t}{-}{1}\right){+}{\mathrm{_C1}}$ (2)

Compatibility

 • The Student[ODEs][Solve][FirstOrder] command was introduced in Maple 2021.
 • The Student[ODEs][Solve][FirstOrder] command was updated in Maple 2022.
 • The output option was introduced in Maple 2022.
user
The text passage describes a Maple command for solving first-order ordinary differential equations (ODEs) and provides an example of its usage.

TYPE: NO_QUESTION

The passage does not contain a mathematical question that requires an answer. It is a description of a Maple command and an example of how to use it. The example shows the command being used to solve a specific ODE, but it is presented as an illustration rather than a question to be answered.