Maple Worksheet for Section 2.1 Problems 1, 3, 11: Draw the direction field (then make observations about the behavior of the solutions): QyQtSSV3aXRoRzYiNiNJKERFdG9vbHNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI= QyQ+SSVERTAxRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRiwiIiQsJkYvRjAtSSRleHBHRiU2IywkRi8hIiNGMEYw QyQ+SSVERTAzRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRixGMCwmKiZGL0YwLUkkZXhwRzYkRipJKF9zeXNsaWJHRiU2IywkRi8hIiJGMEYwRjBGMEYw QyQ+SSVERTExRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRixGMCwkLUkkc2luR0YlNiMsJEYvIiIjIiImRjA= QyQtSStkZmllbGRwbG90RzYiNiZJJURFMDFHRiUtSSJ5R0YlNiNJInRHRiUvRis7ISIjIiImL0YpOyEiJSIiJSIiIg== QyQtSStkZmllbGRwbG90RzYiNiZJJURFMDNHRiUtSSJ5R0YlNiNJInRHRiUvRis7ISIjIiImL0YpOyEiJSIiJSIiIg== QyQtSStkZmllbGRwbG90RzYiNidJJURFMTFHRiUtSSJ5R0YlNiNJInRHRiUvRis7ISIjIiIqL0YpOyEiJyIiJy9JKGRpcmdyaWRHRiU3JCIjSUY3IiIi Problems 21, 24: QyQ+SSVERTIxRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRiwjISIiIiIjLCQtSSRjb3NHRiVGLkYzRjA= QyQ+SSVERTI0RzYiLywmKiZJInRHRiUiIiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJTYjRilGKUYqRioqJiwmRilGKkYqRipGKkYvRipGKiwkKiZGKUYqLUkkZXhwRzYkRi1JKF9zeXNsaWJHRiU2IywkRikhIiJGKiIiI0Yq QyQtSStkZmllbGRwbG90RzYiNiZJJURFMjFHRiUtSSJ5R0YlNiNJInRHRiUvRis7ISIjIiInL0YpOyEiJSIiJSIiIg== QyQtSStkZmllbGRwbG90RzYiNiZJJURFMjRHRiUtSSJ5R0YlNiNJInRHRiUvRis7JCIiIiEiIyIiJS9GKTshIiVGMUYv Problem 27: Find the first local max of the solution to the given DE: QyQ+SSVERTI3RzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRiwjRjAiIiMsJC1JJGNvc0c2JEYqSShfc3lzbGliR0YlRi5GMkYw QyQ+SSRZMjdHNiItSSdkc29sdmVHRiU2JDwkSSVERTI3R0YlLy1JInlHRiU2IyIiISEiIi1GLTYjSSJ0R0YlIiIi Y27 above is the solution to the IVP- Now we find its first local max by setting the derivative to zero: QyQ+SSNkeUc2Ii1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSRyaHNHRig2I0kkWTI3R0YlSSJ0R0YlIiIi Before solving, let's look at a picture and get an estimate: QyQtSSVwbG90RzYiNiRJI2R5R0YlL0kidEdGJTsiIiEiIiQiIiI= QyQ+SSV0c29sRzYiLUknZnNvbHZlR0YlNiQvSSNkeUdGJSIiIS9JInRHRiU7RisiIiMiIiI= QyQtSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJXN1YnNHRiU2JC9JInRHNiJJJXRzb2xHRiwtSSRyaHNHRiU2I0kkWTI3R0YsIiIi Problem 29: Find where the solution crosses y=12 for the first time. QyQ+SSVERTI5RzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYvIiIiRiwjRjAiIiUsJiIiJEYwLUkkY29zRzYkRipJKF9zeXNsaWJHRiU2IywkRi8iIiNGO0Yw QyQ+SSRZMjlHNiItSSdkc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JDwkSSVERTI5R0YlLy1JInlHRiU2IyIiIUYyLUYwNiNJInRHRiUiIiI= QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJi1JJHJoc0dGJjYjSSRZMjlHRigiIiIhIzdGLy9JInRHRig7IiImIiM2Ri8= QyQtSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC8sJi1JJHJoc0dGJjYjSSRZMjlHRigiIiIhIzdGMCIiIS9JInRHRig7JCIjKSohIiIkIiQtIkY4RjA= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn