<item ident="F2-6504" title="F2 | Separation of variables | ver. 6504"> <itemmetadata> <qtimetadata> <qtimetadatafield> <fieldlabel>question_type</fieldlabel> <fieldentry>essay_question</fieldentry> </qtimetadatafield> </qtimetadata> </itemmetadata> <presentation> <material> <mattextxml> <div class="exercise-statement"> <p> <strong>F2.</strong> </p> <p>Find the solution to the given IVP.</p> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" alt="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" title="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" data-latex="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-statement"> <p> <strong>F2.</strong> </p> <p>Find the solution to the given IVP.</p> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%5Cfrac%7B18%20%5C,%20t%7D%7B%7By%7D%7D%20=%20-3%20%5C,%20%7By%7D%20%7By'%7D%20+%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%202" alt="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" title="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" data-latex="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2"> </p> </div> </mattext> </material> <response_str ident="response1" rcardinality="Single"> <render_fib> <response_label ident="answer1" rshuffle="No"/> </render_fib> </response_str> </presentation> <itemfeedback ident="general_fb"> <flow_mat> <material> <mattextxml> <div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20%5Csqrt%7B3%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20-%2012%7D" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}"> </p> </div> </mattext> </material> </flow_mat> </itemfeedback> </item>